Question

At the beginning of the year 1995 , the population of Townsville was 3264 . By the beginning of the year 2014 , the population had reached 4543. Assume that the population is growing exponentially, answer the following.

Estimate the population at the beginning of the year 2019.

Answer 1

To estimate Townsville's population for the year 2019, we calculate the exponential growth rate from 1995 to 2014 data and use it in the exponential growth formula for the additional five years.

Step-by-step explanation:

To estimate the population at the beginning of the year 2019, given that the population is growing exponentially, we first determine the rate of growth using the exponential population growth formula:

P(t) = P_0 * e^(rt)

Where:

• P(t) is the population at time t
• P_0 is the initial population size
• r is the growth rate
• t is the time in years

Given that the population of Townsville was 3264 at the beginning of 1995 and grew to 4543 by the beginning of 2014, we can use these values to solve for r. After finding r, we can then predict the population for the year 2019.

Let's go through the steps:

1. Calculate the number of years between 1995 and 2014, which is 19 years.
2. Set up the equation 4543 = 3264 * e^(19r) and solve for r.
3. Using the growth rate r, predict the population for 2019 by setting t to 24 years (from 1995 to 2019) in the exponential growth formula.

This process will give us the estimated population at the beginning of 2019.